Blurry Render for a Character
I believe this boils down to the way Blender displays pixels. It attempts to blend them together to make low-res textures less obvious. 
You can set how Blender blends pixels together in the material node editor, on the image texture node.
By default, Blender sets pixel blending to "Linear." This blending mode will result in the blurry effect you want to get rid of.

Setting the  blending mode to "Closest" will allow for the sharp pixels I assume you are after.
Hope this helped!